Let us now turn to the application of this result to étale cohomology of rigid spaces. Recall that for any rigid space \(X/K\) , work of Huber [1]} and Berkovich [2]} shows that the derived category \(D(X,\mathbf {Z}/n)\)  of étale \(\mathbf {Z}/n\) -sheaves admits a reasonable 6-functor formalism (at least for \(n\)  invertible on \(K\) ). However, unlike in the case of schemes, it is much more subtle to isolate a reasonable subcategory of “constructible” complexes which are stable under the 6 operations.For instance, constructible sheaves in the sense of Huber's work [1]}, while having many wonderful categorical properties, do not capture the same geometric intuition as the corresponding notion in algebraic or complex geometry. Indeed, even the skyscraper sheaf at a classical point, perhaps the simplest example of a proper pushforward, is not Huber-constructible. Relatedly, analytifications of algebraically constructible sheaves on algebraic varieties are almost never Huber-constructible. In [4]}, the second author proposed that the following notion should yield the desired theory.
